Vol. 14, No. 9, 2020

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The Prasad conjectures for $\mathrm{GSp}_4$ and $\mathrm{PGSp}_4$

Hengfei Lu

Vol. 14 (2020), No. 9, 2417–2480
Abstract

We use the theta correspondence between GSp4(E) and GO(V ) to study the GSp4-distinction problems over a quadratic extension EF of nonarchimedean local fields of characteristic 0. With a similar strategy, we investigate the distinction problem for the pair (GSp4(E),GSp1,1(F)), where GSp1,1 is the unique inner form of GSp4 defined over F. Then we verify the Prasad conjecture for a discrete series representation τ̄ of PGSp4(E).

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Keywords
Langlands correspondence, see-saw diagrams, theta lift, quaternionic Hermitian groups, the Prasad conjecture
Mathematical Subject Classification 2010
Primary: 22E50
Secondary: 11F27
Milestones
Received: 7 May 2019
Revised: 8 February 2020
Accepted: 4 May 2020
Published: 13 October 2020
Authors
Hengfei Lu
Department of Mathematics
Weizmann Institute of Science
Rehovot
Israel
Department of Mathematics
University of Vienna
Vienna
Austria